Tensorflow Convolution Neural Network with differe

I am attempting to create a deep CNN that can classify each individual pixel in an image. I am replicating architecture from the image below taken from this paper. In the paper it is mentioned that deconvolutions are used so that any size of input is possible. This can be seen in the image below.

Github Repository

Currently, I have hard coded my model to accept images of size 32x32x7, but I would like to accept any size of input. What changes would I need to make to my code to accept variable sized input?

 x = tf.placeholder(tf.float32, shape=[None, 32*32*7])
 y_ = tf.placeholder(tf.float32, shape=[None, 32*32*7, 3])
 ...
 DeConnv1 = tf.nn.conv3d_transpose(layer1, filter = w, output_shape = [1,32,32,7,1], strides = [1,2,2,2,1], padding = 'SAME')
 ...
 final = tf.reshape(final, [1, 32*32*7])
 W_final = weight_variable([32*32*7,32*32*7,3])
 b_final = bias_variable([32*32*7,3])
 final_conv = tf.tensordot(final, W_final, axes=[[1], [1]]) + b_final

回答1:

Dynamic placeholders

Tensorflow allows to have multiple dynamic (a.k.a. None) dimensions in placeholders. The engine won't be able to ensure correctness while the graph is built, hence the client is responsible for feeding the correct input, but it provides a lot of flexibility.

So I'm going from...

x = tf.placeholder(tf.float32, shape=[None, N*M*P])
y_ = tf.placeholder(tf.float32, shape=[None, N*M*P, 3])
...
x_image = tf.reshape(x, [-1, N, M, P, 1])

to...

# Nearly all dimensions are dynamic
x_image = tf.placeholder(tf.float32, shape=[None, None, None, None, 1])
label = tf.placeholder(tf.float32, shape=[None, None, 3])

Since you intend to reshape the input to 5D anyway, so why don't use 5D in x_image right from the start. At this point, the second dimension of label is arbitrary, but we promise tensorflow that it will match with x_image.

Dynamic shapes in deconvolution

Next, the nice thing about tf.nn.conv3d_transpose is that its output shape can be dynamic. So instead of this:

# Hard-coded output shape
DeConnv1 = tf.nn.conv3d_transpose(layer1, w, output_shape=[1,32,32,7,1], ...)

... you can do this:

# Dynamic output shape
DeConnv1 = tf.nn.conv3d_transpose(layer1, w, output_shape=tf.shape(x_image), ...)

This way the transpose convolution can be applied to any image and the result will take the shape of x_image that was actually passed in at runtime.

Note that static shape of x_image is (?, ?, ?, ?, 1).

All-Convolutional network

Final and most important piece of the puzzle is to make the whole network convolutional, and that includes your final dense layer too. Dense layer must define its dimensions statically, which forces the whole neural network fix input image dimensions.

Luckily for us, Springenberg at al describe a way to replace an FC layer with a CONV layer in "Striving for Simplicity: The All Convolutional Net" paper. I'm going to use a convolution with 3 1x1x1 filters (see also this question):

final_conv = conv3d_s1(final, weight_variable([1, 1, 1, 1, 3]))
y = tf.reshape(final_conv, [-1, 3])

If we ensure that final has the same dimensions as DeConnv1 (and others), it'll make y right the shape we want: [-1, N * M * P, 3].

Combining it all together

Your network is pretty large, but all deconvolutions basically follow the same pattern, so I've simplified my proof-of-concept code to just one deconvolution. The goal is just to show what kind of network is able to handle images of arbitrary size. Final remark: image dimensions can vary between batches, but within one batch they have to be the same.

The full code:

sess = tf.InteractiveSession()

def conv3d_dilation(tempX, tempFilter):
  return tf.layers.conv3d(tempX, filters=tempFilter, kernel_size=[3, 3, 1], strides=1, padding='SAME', dilation_rate=2)

def conv3d(tempX, tempW):
  return tf.nn.conv3d(tempX, tempW, strides=[1, 2, 2, 2, 1], padding='SAME')

def conv3d_s1(tempX, tempW):
  return tf.nn.conv3d(tempX, tempW, strides=[1, 1, 1, 1, 1], padding='SAME')

def weight_variable(shape):
  initial = tf.truncated_normal(shape, stddev=0.1)
  return tf.Variable(initial)

def bias_variable(shape):
  initial = tf.constant(0.1, shape=shape)
  return tf.Variable(initial)

def max_pool_3x3(x):
  return tf.nn.max_pool3d(x, ksize=[1, 3, 3, 3, 1], strides=[1, 2, 2, 2, 1], padding='SAME')

x_image = tf.placeholder(tf.float32, shape=[None, None, None, None, 1])
label = tf.placeholder(tf.float32, shape=[None, None, 3])

W_conv1 = weight_variable([3, 3, 1, 1, 32])
h_conv1 = conv3d(x_image, W_conv1)
# second convolution
W_conv2 = weight_variable([3, 3, 4, 32, 64])
h_conv2 = conv3d_s1(h_conv1, W_conv2)
# third convolution path 1
W_conv3_A = weight_variable([1, 1, 1, 64, 64])
h_conv3_A = conv3d_s1(h_conv2, W_conv3_A)
# third convolution path 2
W_conv3_B = weight_variable([1, 1, 1, 64, 64])
h_conv3_B = conv3d_s1(h_conv2, W_conv3_B)
# fourth convolution path 1
W_conv4_A = weight_variable([3, 3, 1, 64, 96])
h_conv4_A = conv3d_s1(h_conv3_A, W_conv4_A)
# fourth convolution path 2
W_conv4_B = weight_variable([1, 7, 1, 64, 64])
h_conv4_B = conv3d_s1(h_conv3_B, W_conv4_B)
# fifth convolution path 2
W_conv5_B = weight_variable([1, 7, 1, 64, 64])
h_conv5_B = conv3d_s1(h_conv4_B, W_conv5_B)
# sixth convolution path 2
W_conv6_B = weight_variable([3, 3, 1, 64, 96])
h_conv6_B = conv3d_s1(h_conv5_B, W_conv6_B)
# concatenation
layer1 = tf.concat([h_conv4_A, h_conv6_B], 4)
w = tf.Variable(tf.constant(1., shape=[2, 2, 4, 1, 192]))
DeConnv1 = tf.nn.conv3d_transpose(layer1, filter=w, output_shape=tf.shape(x_image), strides=[1, 2, 2, 2, 1], padding='SAME')

final = DeConnv1
final_conv = conv3d_s1(final, weight_variable([1, 1, 1, 1, 3]))
y = tf.reshape(final_conv, [-1, 3])
cross_entropy = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(labels=label, logits=y))

print('x_image:', x_image)
print('DeConnv1:', DeConnv1)
print('final_conv:', final_conv)

def try_image(N, M, P, B=1):
  batch_x = np.random.normal(size=[B, N, M, P, 1])
  batch_y = np.ones([B, N * M * P, 3]) / 3.0

  deconv_val, final_conv_val, loss = sess.run([DeConnv1, final_conv, cross_entropy],
                                              feed_dict={x_image: batch_x, label: batch_y})
  print(deconv_val.shape)
  print(final_conv.shape)
  print(loss)
  print()

tf.global_variables_initializer().run()
try_image(32, 32, 7)
try_image(16, 16, 3)
try_image(16, 16, 3, 2)

回答2:

Theoretically, it's possible. you need to set the image size of the input and label image place holder to none, and let the graph dynamically infer the image size from input data.

However, have to be careful when you define the graph. Need to use tf.shape instead of tf.get_shape(). the former dynamically infer the shape only when you session.run, the latter can get the shape when you define the graph. But when input size is set to none, the latter does not get true reshape (maybe just return None).

And to make things complicated, if you use tf.layers.conv2d or upconv2d, sometimes these high level functions do not like tf.shape, because it seems they assume the shape information are available during graph construction.

I hope I have better working example to show the points above. I'll put this answer as a placeholder and will come back and add more stuff if I get a chance.